Cities, Wages, and the Urban Hierarchy. Abstract

Transcription

1 Cities, Wages, and the Urban Hierarchy Juan Soto Department of Economics Universidad Católica del Norte Dusan Paredes Department of Economics Universidad Católica del Norte Regional Economics Application Laboratory University of Illinois, Illinois, USA Abstract We present evidence regarding the unequal spatial distribution of population in the north and south of Chile which implies that even when geographical distances to the main urban center are similar, the distances in a context of urban hierarchy are completely different. Given this economic geography, we postulate that Central Place Theory provides a better understanding for the study of city size wage gap in Chile. In order to test our hypothesis, we construct five tiers of urban hierarchy using the 2002 National Census and then contrast the effect generated by the urban hierarchy on worker wages using nine waves of the National Socioeconomic Characterization Survey (CASEN). Keywords: Labor productivity, amenities, urban hierarchy. The authors acknowledge and appreciate the work of Rose Olfert, Miguel Atienza, Marcelo Lufin, Victor Iturra who all reviewed the paper, and the financial support of Chilean Fondecyt [ ] Understanding income inequality persistency and its spatial dimension in Chile. The authors are also appreciative to the Chilean Science Funding CONICYT Apoyo a la Formación de Redes Internacionales entre Centros de Investigación 2012 [Redes ]. 1

2 Introduction The dynamic evolution of city size, which is defined as the spatial unit where a person is working inevitably affects the wages of its inhabitants. According to empirical findings, a larger city size corresponds with a higher nominal wage. In fact, this regularity has merited its own definition within various other works, being referred to as Urban Wage Premium (UWP) [9] as well as city size wage gap [19]. In addition to amenities and cost of living as relevant factors [17, 18], there is a certain agreement on the fact that productivity is the key link between wages and city size, although it is still controversial how this effect is carried out [7]. For example, localization economies argue that larger cities present a higher spatial proximity of firms belonging to a similar industry which in turn improves the level of knowledge spillovers as well as incentivizing the specialization of labor markets which generates greater productivity at an intra-industry level [11]. Alternatively, the urbanization economies would also result in better physical structures, such as public infrastructure, implying an increase in the level of productivity, but at an inter-industry-level [10, 11]. Other theoretical frameworks sustain that the economies of scale derived from an increasing return to scale, namely a continuous reduction of fixed costs along with increased production in order to supply large cities, have direct repercussions on firm productivity [8]. Most of these theoretical arguments designate the city size as the engine behind productivity. However, with scarce attention paid to the urban hierarchy of those cities, or without the consideration of the remoteness level among the spatial units this conclusion is incomplete. We suppose then, that the only relevant hierarchy to explain the wage differential is the size rank. However, this variable is spatially blind in the sense that even larger cities could be remotely located in the urban system, something that would reduce their role as a source of productivity [16]. To understand the differences between city-size and urban-hierarchy, we pay attention to the original definition of the Central Place Theory (CPT) [3]. Following the explanation provided by [16], we assume that two cities both of which present a similar geographical distance to the largest city of the urban hierarchy, let s say they are located 1,000 km in opposite directions to the biggest city in the urban system, as Figure 1 shows. City D and city C are each the same size, but city D does not have an intermediate city between itself and the main urban center (city A), and oppositely, city C has access to city B if 2

3 it moves in the direction of the large city. Note that even when the geographical distance between these cities and the largest urban center is similar, the intermediate city offers a greater number of services to city C and thus would be a recipient of agglomeration economies through commutation opportunities [4]. Therefore, city size (or city size rank) alone, by way of the implied productivity levels, may not be sufficient to explain spatial wage differentials. The city size rank could be reflective of productivity differences due to agglomeration economies, while departures from the predicted wage differences due to size rank may reflect the premium required to compensate the household/labor for the role played by amenities. FIG. 1: Hierarchy and size of cities Small City (D) Big City (A) M edium City (B) Small City (C) Note: The figure shows that city size is not enough to characterize wage disparities, since we expect a differentiated effect over city D and city C. Because between city C and city A there is an intermediate size city (B) and city C can benefit of services that are in city B by commutation but city D have to commute only to city A for access to more services. Source: Authors. We argue that our proposal of an urban hierarchy as an explanatory variable of local wages is especially relevant in countries that are characterized by factors such as high levels of spatial concentration in a metropolitan area as well as the existence of remote regions with an asymmetrical spatial distribution of cities. A fitting example of these characteristics is Chile. The country is essentially a natural experiment in testing our hypothesis due to its unique geography, which is 4,270 km long and has a maximum width of 445 km, implying high transportation costs and an extreme spatial concentration around a unique city [14]. This concentration involves the city of Santiago in the Metropolitan Region (MR), which is paradoxically located at the middle point of the country. According to Figure 2, in 1885 the MR had nearly the same share of population as the other regions. However, this share has grown disproportionally over the last century. In 2002 the MR represented approximately 40% of the total population while consisting 3

4 FIG. 2: Population Interregional Distribution. Note: The figure shows the unequal density of cities in Chile between the north and the south of the country. This pattern of population distribution arise around 50 s and at 2002 the Metropolitan Region concentrates 40% of the population. Source: Authors. of just 2% of the total physical territory. Meanwhile, the north represented 22% of the population and the south 38%. This evolution in the formation of cities has produced an unequal density in which the south has a ratio of almost three cities to one compared to the north. This fact leads to more remote northern cities, and the more remote a city is, the more difficult it is to access services and thus the lower the rank in the city hierarchy. Of interest, region II of Chile is the world leader in copper production with a significant level of foreign direct investment. This implies than region II is a productive pole, but it is also highly remote 4

5 in the urban system. Thus, the region is perceived as a disamenity, not only by workers but also by mining firms who must willing to pay higher wages to attract the necessary human capital [1]. Therefore, remote cities located in the north should be compensated with higher wages even after holding constant the size and economic prosperities of those cities. Thus, our hypothesis establishes that a higher spatial disconnection implies disamenities not only for workers but also for firms which will have reduced access to services and must offer higher wages in order to be attractive to both local and national workers. With this purpose, we estimate the size of the wage premiums required to offset the remoteness incurred by workers over and above the city-size productivity effects. In order to test our hypothesis, we use wages at the worker level in Chile using a pool of nine waves of the National Socioeconomic Characterization Survey (CASEN) from 1992 to We require four steps to carry out our empirical testing. First, we create five levels of urban hierarchy using the city definition of the Chilean National Institute of Statistics (INE) and the last available census (2002), namely a tier 1 formed by the main urban center of 5.6 million inhabitants, a tier 2 formed by two cities with at least 800 thousand inhabitants, a tier 3 formed by cities with at least 200 thousand inhabitants, a tier 4 formed by cities with at least 100 thousand inhabitants and finally a tier 5 formed by cities with less than 100 thousand inhabitants. Second, in order to show that city size rank is not sufficient to explain spatial wage differentials, we estimate the city size wage gap in order to contrast it with the expected theoretical prediction: the higher the size of the urban tier, the higher the wages. Third, we define our conception of urban hierarchy as understood from Christaller`s CPT and then compute our empirical approximation of the urban hierarchy as incremental distance [16]. Fourth, we estimate the effect of the incremental distance over worker wages. This compares the size of the premium for living in a larger city with the remoteness from intermediate-size urban amenities as well as remoteness from the top of the hierarchy correcting for the previous city size wage gap estimation. We refer to this as the urban hierarchy wage gap and we compare these effects over cities in the north and the south of Chile. In section 2, we discuss the existing literature on city size wage gap and Central Place Theory in detail. In section 3 we present our methodology followed by data in section 4. Section 5 presents and discusses the results and section 6 concludes and provides some ideas for future research. 5

6 Theoretical Framework There are several theories to understand why denser cities affect wages positively and most of them point directly toward productivity. The Spatial Equilibrium Model (SEM) proposes that the spatial differences of wages are also a compensatory mechanism to adjust for differentials in housing prices and amenities [17]. In large cities where there is scarce availability of land, workers require higher wages to compensate for higher housing prices. Otherwise, the labor supply cannot maintain a similar utility level to that of an alternative region. On the other hand, given the higher rents paid by firms, they will wish to pay lower wages in order to maintain the same cost structure; otherwise the cost will be increased. This trade-off is adjusted by the amenity effect. For example, workers in cities with amenities should, ceteris paribus, be willing to accept lower nominal wages. However, the final wage effect will be explained by rents. This causal mechanism clearly indicates that in order to understand the wage differential we must first consider the crucial role of amenities. Curiously, most empirical works have not directly addressed the hypothesis of an equal utility level, but rather have focused almost exclusively on analyzing how spatial wage differentials are reduced after controlling for local prices and human capital proxies (see Partridge and Rickman [15] and Partridge et al. [16] for a discussion about this point). The second body of theories postulates that higher skilled workers exist in larger cities [7]. We highlight the word exist because of the lack of consensus regarding whether the city size alone generates higher productivity or rather if it attracts higher productivity workers [6]. If the city size generates higher productivity through economics of agglomeration, then the rate of wage growth in large cities, ceteris paribus, should be significantly higher than small towns [9]. Alternatively, workers who move toward large cities should gain a wage premium in the medium to long run. Additionally, those workers who move outside large cities will most likely bring with them an increased productivity to their new labor markets. If cities attract more productive workers, then they must be automatically compensated with higher wages when they enter a large city, mainly through a price effect that would subsequently vanish if they leave [21]. To explain the contributions of adding the urban hierarchy conceptualization from CPT to city size wage gap literature, Figure 3 shows the spatial behavior of workers and firms on CPT adapted from Clark and Rushton [4]. The figure represents five levels of cities in a 6

7 size-based hierarchy. Under the assumption that workers and firms go to the nearest center in the urban hierarchy and that the greater the urban center the greater the productive diversity, both workers and firms in city D are attracted by city A (where there is a full set of services and amenities available) while workers of city E are attracted by city B (where there is a greater number of services and amenities than city C). Nevertheless, the attraction of city A over city D is greater than the attraction of city B over city E, since city A is 2 levels higher than city B in the urban hierarchy. Therefore, city D and city E are not of the same order in the system of cities as a consequence of city A and city B not being of the same order in a size-based hierarchy of cities. This nature of the spatial system of cities reveals the tendency of a different development between city D and city E, since city D can exploit the large size of city A [4]. In other words, the level of remoteness to the main urban center as well as intermediate size cities is another type of amenity to workers and firms. FIG. 3: The Urban Hierarchy on Central Place Theory. A D E C B Note: The figure shows the spatial behaviour of workers and firms in Central Place Theory. Since workers and firms commute to the nearest center in the hierarchy. Both of them in city D are attracted by city A and workers and firms in city E are attracted by city B, but workers and firms of city D can exploit more the big size of city A than workers and firms in city E. Therefore, city D and city E are not of the same order in the hierarchy of cities in spite that have the same population. Source: Adapted from Clark and Rushton [4]. From the firms perspective, considering the effect of remoteness over the city size wage gap, the company would likewise be able to access the full range of business services and input 7

8 suppliers in the center of the country and at the top of the hierarchy. However, if they are located in a very remote location far from the largest city, they will nevertheless also benefit from access to the types of linkages and services that will be available in intermediate-size cities even though these are not as complete or varied as what would be available at the top of the hierarchy. Therefore, their wage offer would be lower in remote areas because of the higher distance costs, and possibly also because of less competition for labor. Additionally, remote areas might have advantages in productivity due to concentrations of a particular industry (for example the high external demand for copper mining in Chile). On the other hand, from a workers point of view, they likewise would be able to access the complete set of amenities at the main urban center as well. Workers would additionally benefit from access to intermediate size cities, but higher housing prices must also be taken into consideration. Such as we will discuss later, this mechanism could be crucial to understand the case of Chile. The Spatial Equilibrium Model From the Roback [17] model of Spatial Equilibrium, workers maximize U(x, l c ; s) subject to w + I = x + l c r. Where x is the amount of commodity consumed, l c the residential land used, s in the original model is the level of the amenity, which in our case is the remoteness of the city from the system, w the wage and r the rent. Therefore, the equilibrium condition for the representative worker is represented in equation (1): V (w, r; s) = k (1) which establishes that given a level of remoteness, wages and rents must be adjusted to equalize utility level in all cities, otherwise people will have incentives to move out. V/ s < 0 since s is an unproductive amenity. On the other hand, firms minimize C(w, r; s) subject to X = f(l p, N; s), which assumes constant returns to scale. l p is the land used for production and N the total number of workers in the city. The firms equilibrium condition is given by the unity cost function in equation (2): C(w, r; s) = 1 (2) 8

9 which is strictly increasing by components. The total differential of (1) and (2), and solving for dw/ds and dr/ds, gives equations (3) and (4). dw ds = 1 (V (r)c (s) C (r)v (s)) 0 (3) dr ds = 1 (C (w)v (s) C (s)v (w)) < 0 (4) where = C (r)v (w) V (r)c (w) > 0. Under the assumption that remoteness is an unproductive amenity, which is especially true for firms, the variation on rents due to an increase in s will always be dr/ds < 0 ceteris paribus. However, the sign of dw/ds is uncertain and would be determined by the numerator of (3). Therefore, in order to observe the expected city size wage gap V (r)c (s) < C (r)v (s) must be met. Thus the relative variation of a workers utility to remoteness and the firms utility to rents must be greater than the change in a workers utility to rents and remoteness over the firms costs. Otherwise we would expect a non-negative gradient of wages as city size increases. Equilibrium conditions are represented by isoutility and isocost function in Figure 4, where also is represented the difference in wages between two cities, on which remoteness of city 2 is higher than remoteness of city 1 (s 2 > s 1 ). There is an equilibrium in A with wage w 1 and rent r 1, in which the indirect utility function v 1 (w, r, s 1 ) is equalized to the cost function of the firm c 1 (w, r, s 1 ), otherwise firms and workers would have incentives to move out. Therefore, the firm effect of an increase in remoteness over wages produce a wage w 2 and a rent r 2 in the point B. However, once considering workers valuation of remoteness, the equilibrium is the point C with wage w 3 and rent r 3. Then, the final effect on wages between city 1 and city 2 would be the difference w 1 w 3. Thus, the remoteness effect on rents is clear while the effect on wages is uncertainly. Because the remoteness effect on wages also depends on the distance to other urban centers. Methodology We now proceed to explain each step of the empirical exercise in which we estimate the relationship between urban hierarchy and wages. As far as the authors know, this is the first incorporation of urban hierarchy in a study regarding Chile. In spite of the attractiveness of this work though, we must accept that our data is far from that of an ideal experiment. For example, ideally we would be working with an extensive data series pertaining to regional 9

10 w FIG. 4: Remoteness Effect on Wages and Rents. s 1 < s 2 V (w, r; s 2 ) V (w, r; s 1 ) 1 w 3 w 2 C B A C (w, r; s 2 ) C (w, r; s 1 ) r 3 r 2 r 1 r Note: The figure shows the effect of remoteness over wages and rents. Clearly the effect on rents always is negative, since remoteness is an unproductive amenity. However the sign in wages is unclear an is determined by the sign of V (r)c (s) C (v)v (s). The last determine the expected city size wage gap. Source: Adapted from Roback [17]. wages for workers; however, data is available from only the 1990 s. Additionally, Chile does not report a spatial price index and there is no official indicator regarding how expensive a particular county (or even state) is with respect to the rest of the country (See Paredes and Iturra [14] or Paredes [13] for a deeper discussion). This constraint implies that special warnings must be considered in the estimation, and, in some way, a type of control by local index prices should also be incorporated. As is the case in most developing countries, Chile has no surveys with a testing score for some proxy of skill and the only data with national coverage contains only standard variables for human capital. Alternative procedures such as panel data that might be used to control for unobservable ability are also ruled out as this panel data exists only for three of the regions and there exists serious doubts regarding 10

11 its accuracy. However, this lack of information only reinforces the motivation behind this paper; we have a clear conviction that serious efforts must be carried out in order to provide acceptable evidence regarding the gap. Urban Hierarchy According to the Chilean National Institute of Statistics (INE), the administrative division of the geographical territory is composed of three levels of aggregation. By 2014, there was a higher aggregate level formed by 15 regions, which are subdivided in 54 provinces and 346 communes. By default, our city definition is equivalent to a county. We are conscious of the difference between working with these functional areas instead of the administrative division, especially when analyzing spatial labor markets. For this reason we have decided to include the functional division of the XVII National Population Census of 2002, which includes the conurbations previously indicated [2]. From there we redefine the administrative division as conurbations, leaving us with 275 functional areas from 346 communes, and then we must divide the cities into groups according to their size. In this second step, we clearly observe breaks in the size distribution of cities (see Figure 5) which allows us to define urban tiers. These are representative over time, as the size distribution of cities between 1970 and 2002 is almost identical with no significant changes in the hierarchy [20]. At this point we construct five groups of cities based on their size (see Figure 6). The first is the reference group and is the conurbation of Santiago, formed by the union of 37 communes; this functional area had a population of 5,631,839 inhabitants in Next, we have four comparison groups. The group of large cities, which is formed by two conurbations, the Concepcion Area with a 2002 population of 848,023 inhabitants and the Valparaiso Area, with 824,006. From there we generate two groups of intermediates cities. The first is formed by seven cities whose population is between 296,253 and 208,907 inhabitants. The second is formed by cities and conurbations with a population between 175,441 and 104,124. Finally, we define the group of small cities, which have a population below 104, communes compose this final category. 11

12 FIG. 5: City Size Distribution. Note: The figure shows the highly concentrated Chilean city size distribution at the last available census of Source: Authors. Incremental Distance For our Urban Hierarchy approximation, we follow the lead of Partridge et al. [16], by using incremental distance. This is computed as the minimal road distance between functional areas belonging to different tiers, minus the distance between cities of an intermediate hierarchy. For example, as Figure 7 shows, the tier 2 southern city Concepcion is located 512 km from the only tier 1 functional area Santiago. Meanwhile, tier 3 city La Serena in the north is located 555 km from Santiago. However, between La Serena and Santiago is Valparaiso (the city is 420 km from La Serena), which is another tier 2 city. Valparaiso offers certain services that are not available in La Serena, and inhabitants in La Serena would have to travel only 135 km to Santiago in order to have access to the services that Santiago offers but not Valparaiso. Note the implicit assumption that tier 1 offers all the services of minor urban tiers. Therefore, the incremental distance to tier 1 for Concepcion is 512 km, but for La Serena it is 135 km, which is the previous distance to Santiago minus the distance to Valparaiso. The incremental distance to tier 2 for La Serena is 420 km. We choose the incremental distance because this variable better represents the concept 12

13 FIG. 6: Urban Tiers. Note: The figure shows the spatial distribution of the five size levels of cities hierarchy created across the north, center and the south of the country from left to right. Source: Authors. established by Christaller [3] in his Central Place Theory as an embedded hierarchy of cities. Regarding the density of cities, it also permits the incorporation of the heterogeneity between the north and the south, something that we believe, coupled with the fact that Santiago is at the center of the national territory, has important implications over the spatial wage gap. Using the incremental distance, we capture the marginal effect of having access to successively higher order cities in the system, as a proxy of a successively higher number of services. Nevertheless, as Partridge et al. [16] notes, incremental distance interpreted in a sense of remoteness from the system of cities can have ambiguous effects on wages as this depends on the magnitudes of firm and worker responses to remoteness. If workers, due to 13

14 FIG. 7: Incremental Distance. Note: The figure shows an example of the empirical implementation of remoteness as the incremental distance variable from Partridge et al. [16]. In this, La Serena is at 555km by road from Santiago. But between La Serena and Santiago there is Valparaiso. Therefore, since Valparaiso is an intermediate size city between La Serena and Santiago, the marginal distance (Incremental distance to tier 1) for La Serena is 135km. However, the incremental distance to tier 1 for Concepción is 512km, since there are not intermediate size cities between Concepción and Santiago. Source: Authors. congestion in large centers, positively perceive remoteness, then we may expect a negative effect on wages. But if remoteness is perceived as a disamenity, we might expect a positive effect on wages if a city is more disconnected from the system of cities. We know that this effect could be different for each of the tiers previously defined. Additionally, we realize that 14

15 the size difference between tier 1 and the following tiers is substantial and thus results be considered with caution. Data We pursue our objective using information from nine cross sectional Socio-Economic National Characterization (CASEN) surveys available from the years 1992, 1994, 1996, 1998, 2000, 2003, 2006, 2009 and Originally, the appended surveys contained 1,870,065 observations of which 639,701 of them reported a positive wage. The surveys showed outliers with wages that were either unrealistically high or well below the minimum wage. We decided to get rid of the 0.5% lowest and highest values on the variable wages for each year, maintaining 633,256 observations. Other scenarios taken into consideration were the 4,841 workers that reported missing or zero worked hours as well as the 4,679 workers that declared to have worked more than 672 hours per month, which is physically impossible. These filters reduce the sample to 623,736 observations. Originally, the survey showed ten occupational categories, but military forces were taken out because their wages are not traded in standard labor markets (1,952 observations). Another filter maintained only those observations for workers between 14 and 65 years of age, resulting in a sample of 602,142 observations. Besides the wages, we also have to treat the outliers and missing values in the control variables, which reduces our sample to 540,845 observations. Table 1 presents the descriptive statistics of some of the relevant variables used in the econometric analysis. Econometric Concerns Our empirical strategy first focuses on the city size wage gap estimation. As Combes et al. [5] suggest, we follow a simple model in which city size increases wages through an increase in the marginal product of labor (worker characteristics) or by differences in amenities and housing costs across cities (cities characteristics). The wage of the worker i in a city c is given by: log w ic = α log pop c + η c + µ i + ɛ ic (5) where pop c is the population in the city c, η c is a city effect, µ i a worker effect and ɛ ic a component for the shock of the worker i in the city c. However, if we do not observe city or 15

16 TABLE I: Summary statistics of wages and remoteness by urban tiers Tier 1 Tier 2 Tier 3 Tier 4 Tier 5 Total Log of wages (0.867) (0.878) (0.920) (0.899) (0.835) (0.870) Incremental distance: to tier (163) (140) (177) (176) (185) to tier (662) (551) (321) (399) to tier (629) (262) (298) to tier (191) (149) Note: Mean and standard deviation (in parentheses). worker effects these enter in the error term and hence: Cov(log pop c(i), η c(i) + µ i + ɛ ic(i) ) = Cov(log pop c(i), η c(i) ) +Cov(log pop c(i), µ i ) + Cov(log pop c(i), ɛ ic(i) ) (6), considering c(i) the city of worker i. Therefore, to obtain an unbiased estimation of α, (6) must be equal to zero. But Cov(log pop c(i), η c(i) ) 0 since log pop c = β log w c + µ c and log w c = α log pop c + η c by endogeneity. Then log pop c = (βη c + µ c )/(1 + αβ) with αβ < 1. Leading to Cov(log pop c, η c ) = βv ar(η c) + Cov(η c, µ c ) (1 αβ) (7),which is equal to zero if V ar(η c ) = 0 i.e. there should not be observable characteristics of cities that increase wages and increase city population (amenities) and Cov(η c, µ c ) = 0 i.e. city characteristics will not be correlated with worker characteristics in cities (spatial labor sorting). Continuing on a different vein, some exogenous shocks of productivity may yield to Cov(log pop c, ɛ ic ) 0. For this reason, we introduce additional controls to avoid the bias of the population coefficient. 16

17 Estimation An approximation estimation for Eq. (5) is estimated by OLS and presented in the results as Model 1: r k h log w i = α 0 + α 1 log pop c + γ r η c + β k +θ h D h + ɛ i (8) r=1 k=1 h=1 where city effects (η c,r ) incorporates: annual mean temperature, annual precipitation, the coefficient of the variation of precipitation, the log of the average elevation of land and the log of its standard deviation [22] [23], the inverse of the Hischman-Herfindhal index for economic activity concentration, the Krugman specialization index for employment, and a dummy if the functional area is rural or urban. Worker effects (µ i ) incorporate: age, sex, marital status, years of schooling, and occupation. Finally, we include dummies for year (D h ) in order to capture exogenous temporal shocks. We do not estimate regressions by year in order to avoid a loss of observations and hence representativeness of small communes. Model 2 incorporates four dummies for the size-based hierarchy of cities previously defined as tier l : l log w i = α 0 + α 1 log pop c + δ l + tier l + γ r r l=1 r=1 η c,r (9) k h +β k µ i,k + θ h D h + ɛ i k=1 h=1 Models 1 and 2 do not consider the position of the city in the spatial system of cities and in Model 3 (Eq. 10) we evaluate the role of the spatial system of cities on worker wages including the incremental distance variable (incdist j ), which is composed of four types of distances, which also corrects for V ar(η c ) = 0. l j log w i = α 0 + α 1 log pop c + δ l tier l + τ j incdist j r +γ r η c.r + β k l=1 j=1 (10) k h µ i,k + θ h D h + ɛ i r=1 k=1 h=1 To observe the robustness of our results to price variation across areas, Model 4 incorporates the regional housing price index computed by López and Aroca [12]. Although we are aware of the simultaneity problem of adding the housing price index upon estimating wages, we note that this problem is reduced by the fact that this index is at a regional 17

18 level and we estimate wages using microdata. Since this is available only for the years 2000, 2003, 2006, and 2009, we also incorporate the log of the crime rate per 100,000 people [24], which is available from 2000 to In addition, we estimate the effects of remoteness over the north (regions I, II and III) and the south (regions IX, X, XI and XII) incorporating interaction terms on Model 3 for each type of distance (see Table 3). Results Summary statistics in Table 1 tell us something interesting with respect to the wages in tier 2. In spite of it only being an average, we observe that wages in tier 2 are approximately 24% less than wages in tier 1, and 21% and 13% less than those in tier 3 and 4, respectively. This is counterintuitive to the reasoning that a large city size corresponds with high nominal wages. In addition, Table 2 shows estimation results. All signs for the variable controls are in line with theory and most of them are statistically significant, influenced by the large number of observations. From Model 1, the population elasticity of wages is about 3%. However, in Model 2 we do not observe the expected result of the lower the size of the urban tier the higher the average loss in wages, as the coefficient for tier 2 is lower than for tiers 3 and 4. We argue that this result is a product of the special characteristics of the Chilean spatial system of cities, which is extremely concentrated and has a very particular geography, revealing that size is not enough to characterize Chilean wage disparities across cities because this omits the spatial position of the city in the system. Moreover, this result can already be seen in Model 2, where the coefficients do not show a clear city size gradient. Once we add the four types of incremental distance variables in the Model 3 estimate, and hence our conceptualization of the urban hierarchy, this corrects the counterintuitive result for urban tiers coefficients found in the Model 1 estimate and yields an average loss in wages of about 5% for urban tier 2, 8% for tier 3, 10% for tier 4, and 14% for tier 5. This correction allows us to see the positive gradient of wages as the urban tier increases. We call this effect an urban hierarchy wage gap, since it better characterizes the relative importance of a city in the spatial system of cities. This is presented in Figure 8 alongside a city size wage gap estimate over urban tiers that do not have this correction. Our impression is that in places with an uneven geography and high levels of spatial concentration (as is the case of many Latin-American countries) this consideration becomes necessary. 18

19 FIG. 8: City Size Wage Gap and the Urban Hierarchy Effect. Percent Difference on Wages City Size Wage Gap Urban Hierarchy Wage Gap Tier 5 Tier 4 Tier 3 Tier 2 Urban Tier Note: The figure shows the effect of the correction by the hierarchy of cities over the city size wage gap estimation for Chile. We call this as urban hierarchy wage gap, since capture in a better way the position that have each city in the spatial system of cities. Source: Authors. The coefficient estimates from Model 3 and 4 for the incremental distance variable (see Table 2) give us valuable information in understanding what is behind the effects that we observed in wages. The incremental distance represents the marginal cost or benefit for access to a higher order urban center and since it is based on the workers and firms valuation of the distance to higher order urban centers we must be careful with our interpretation. In Model 3 we observe a loss in wages (with respect to turban tier 1) of -4.6% for every 100 km removed as the coefficient for incremental distance to tier 1 shows. Nevertheless, the estimation of coefficients for incremental distance also has positive effects on wages with respect to the incremental distance (100 km) to other urban tiers; 0.1% to tier 2, 1.2% to tier 3, and 2.9% to tier 4. This indicates that remoteness is valued as a disamenity except with regards to tier 1 in which the negative sign indicates that remoteness is valued as an amenity by workers. Our intuition behind this fact is that it is a consequence of the congestion cost 19

20 that arises from tier 1 and the large size difference with respect to other urban tiers. Since tier 1 is about 6 times the size of tier 2, workers in the urban tier 2 prefer to stay there even though they receive a lower wage than if they were to move to a tier 3 city. This is because a worker knows that in the best of the cases they can commute to Santiago (tier 1) and thus capitalize on the wage this effect. The incorporation of the regional housing price index in the estimation of Model 4 reinforces the robustness of our results. Table 3 shows the effects of remoteness in the north and south as an effect of the interaction terms of the incremental distance with the region in Model 3. In line with our argument, the loss in wages due to remoteness for cities in the north (13%) is higher than that of those in the south (3.4%) (see Table 3). In fact, the effect of remoteness for the central part of the country is always negative and increases the smaller the city. For example, the lowest urban tier (tier 5) sees a decrease in wages of approximately 20% with respect to tier 4 (incremental distance to tier 4 is the distance to tier 4). For the north and south, the effect of remoteness to urban tiers 2, 3, and 4 is positive. Chile is thus divided into three natural areas that are completely different in terms of the behavior of the labor market. Conclusion In this study we have introduced the importance of considering a more complex hierarchy of cities in the city size wage gap estimation in order to better understand the case of countries with a high spatial concentration and an uneven geography. We use the case of Chile as an empirical exercise in observing the difference between a city size wage gap estimate and the effects of considering the position that a city has in the system of cities. After defining five urban tiers base on size within a hierarchy of cities, we implement a measure of the remoteness of a city used by Partridge et al. [16] and estimate the size of the wage premium required to offset remoteness in Chile over cities in the north and south. We found that tier 2 cities see a 5% decrease in wages, tier 3, 8.3%, tier 4, 10.3%, and tier 5, 14%, all with respect to the main urban center (tier 1). In addition, we consistently see a loss in wages of approximately 4.6% per 100 km from the main urban center and a differentiated effect across the northern and southern parts of the country. We argue that our consideration deserves special attention from Latin American countries with high levels of spatial concentration and in which the particular characteristics of labor 20

21 markets substantively affect the observed wage gap across cities. Since we consider the idea that the hierarchy is not conceptualized solely based on the population of a city, and in order to better explain the incentives of workers in locating cities that are more connected in the system we can say that future research should be focused on better understanding the relationships between cities. In this sense, a hierarchy-based scheme is not enough to understand the complex relationships between cities at the present time. References [1]Aroca, P. (2001). Impacts and development in local economies based on mining: The case of the chilean ii region. Resources Policy, 27(2): [2]Brown, L. A. and Holmes, J. (1971). The delimitation of functional regions, nodal regions, and hierarchies by functional distance approaches. Journal of Regional Science, 11(1): [3]Christaller, W. (1933). Die zentralen orte in sü ddeutschland. jena: Gustav fischer verlag. (English translation: The Central Places of Southern Germany). [4]Clark, W. A. V. and Rushton, G. (1970). Models of intra-urban consumer behavior and their implications from central place theory. Economic Geography, 46(3): [5]Combes, P. P., Duranton, G., and Gobillon, L. (2011). The identification of agglomeration economies. Journal of Economic Geography, 11: [6]Combes, P.-P., Duranton, G., Gobillon, L., and Roux, S. (2012). Sorting and local wage and skill distributions in france. Regional Science and Urban Economics, 42(6): [7]Combes, P.-P. P., Duranton, G., and Gobillon, L. (2008). Spatial wage disparities: Sorting matters! Journal of Urban Economics, 63(2): [8]Fujita, M., Krugman, P. R., and Venables, A. J. (2001). Regions, and International Trade. The MIT Press. The Spatial Economy: Cities, [9]Glaeser, E. L. and Mare, D. C. (2001). Cities and skills. Journal of Labor Economics, 19(2):

22 [10]Henderson, J. V. (1986). Efficiency of resource usage and city size. Journal of Urban Economics, 19(47-70). [11]Kim, S. (1989). Labor specialization and the extent of the market. The Journal of Political Economy, pages [12]López, E. and Aroca, P. (2012). Estimación de la inflación regional de los precios de la vivienda en chile. El Trimestre Económico, 315: [13]Paredes, D. (2011). A methodology to compute regional housing price index using matching estimators. The Annals of Regional Science, 46(1): [14]Paredes, D. and Iturra, V. (2013). Substitution bias and the construction of a spatial cost of living index. Papers in Regional Science, 92(1): [15]Partridge, M. D. and Rickman, D. S. (2008). Distance from urban agglomeration economies and rural poverty. Journal of Regional Science, 48(2): [16]Partridge, M. D., Rickman, D. S., Ali, K., and Olfert, M. R. (2009). Agglomeration spillovers and wage and housing cost gradients across the urban hierarchy. Journal of International Economics, 78(1): [17]Roback, J. (1982). Wages, rents, and the quality of life. The Journal of Political Economy, pages [18]Roback, J. (1988). Wages, rents, and amenities: Differences among workers and regions. Economic Inquiry, 26: [19]Rosenthal, S. S. and Strange, W. C. (2004). Evidence on the nature and sources of agglomeration economies. Handbook of regional and urban economics, 4: [20]Vallone, A. and Atienza, M. (2012). Concentration, development and evolution of the urban system in chile between 1885 and Documentos de trabajo en economía y ciencia regional, WP [21]Yankow, J. J. (2006). Why do cities pay more? an empirical examination of some competing theories of the urban wage premium. Journal of Urban Economics, 60(2):

23 [22]Hijmans, R.J., S.E. Cameron, J.L. Parra, P.G. Jones and A. Jarvis (2005). Very high resolution interpolated climate surfaces for global land areas. International Journal of Climatology, 25: Available at: [23]Global SRTM 30 arc sec seamless data, version 2, Available at: [24]Undersecretary of Crime Prevention of the Chilean Ministry of Interior and Public Security (2014). Available at: de denuncias y detenciones.html 23

24 TABLE II: Summary statistics of wages and remoteness by urban tiers Regressor Model 1 Model 2 Model 3 Model 4 Coef. Std. Err. Coef. Std. Err. Coef. Std. Err. Coef. Std. Err. Log of population 0.030*** (0.001) 0.007*** (0.001) 0.005*** (0.001) (0.002) Urban tier: City > 824k & < 848k *** (0.005) *** (0.006) (0.009) City > 208k & < 296k *** (0.006) *** (0.006) *** (0.011) City > 104k & < 175k *** (0.006) *** (0.006) *** (0.011) City < 104k *** (0.008) *** (0.008) *** (0.013) Incremental distance: to tier *** (0.001) *** (0.002) to tier *** (4E-04) *** (0.001) to tier *** (0.001) 0.012*** (0.001) to tier *** (0.001) 0.031*** (0.001) City Effects: IHH Inverse 0.050*** (0.002) 0.055*** (0.002) 0.051*** (0.002) 0.051*** (0.002) Krugman index 0.178*** (0.008) 0.159*** (0.008) 0.167*** (0.008) 0.203*** (0.013) Rural area (=1) *** (0.002) *** (0.002) *** (0.002) *** (0.003) Mean temperature *** (5E-05) *** (4E-05) -1E-04* (1E-04) -2E-04 (1E-04) Precipitation -1E-04*** (2E-06) -1E-04*** (2E-06) -7E-06 (4E-06) -1E-05 (5E-06) Std.dev. precipitation *** (3E-05) *** (4E-05) *** (6E-05) *** (9E-05) Log ave. elevation 0.063*** (0.005) 0.074*** (0.005) 0.093*** (0.005) 0.090*** (0.008) Log std.dev. elevation *** (0.005) *** (0.005) *** (0.005) *** (0.007) Log of the crime rate 0.028*** (0.003) Log of housing price 0.279*** (0.012) Worker Effects: Women (=1) *** (0.002) *** (0.002) *** (0.002) *** (0.003) Married (=1) 0.123*** (0.002) 0.124*** (0.002) 0.124*** (0.002) 0.126*** (0.003) Years of scholarity 0.059*** (3E-04) 0.059*** (3E-04) 0.059*** (3E-04) 0.062*** (4E-04) Age 0.059*** (3E-04) 0.010*** (8E-04) 0.010*** (1E-04) 0.010*** (1E-04) Constant 10.43*** (0.019) 10.79*** (0.025) 10.71*** (0.030) 11.11*** (0.047) Observations 540, , , ,792 Adjusted R-squared F-statistic 2E E * p < 0.05, ** p < 0.01, *** p < All estimations also include controls for occupation as well as dummies for year. 24

25 TABLE III: Remoteness effects over regions North South Center Incremental distance to tier *** *** *** (0.008) (0.002) (0.001) Incremental distance to tier *** 0.132*** *** (0.002) (0.004) (0.002) Incremental distance to tier *** 0.089*** *** (0.006) (0.006) (0.005) Incremental distance to tier ** 0.227*** *** (0.018) (0.018) (0.018) * p < 0.05, ** p < 0.01, *** p < Standard error in parentheses. R-square = 0.59 and n=538,